One possibility is for no limits to be placed on the liability of the members of the company for the company's debts.
This means that, if the assets that belong to the company itself are insufficient to pay the company's debts, then the members are liable to make up the shortfall. This obviously exposes the members of the company to great risk. However, such companies are used when the law does not permit more limited liability, such as when members of a profession, such as lawyers, form a company to run a business together.
It is obvious that unlimited companies are very similar to partnerships. The main difference is that an unlimited company can have a single owner, whereas a partnership requires two or more persons.